Consider the material processing experiment of Problem 5.24, with atmospheric nitrogen used to impalement cooling by convection. However, instead of using a prescribed value of the convection coefficient, compute the coefficient from an appropriate correlation.

(a) Neglecting radiation, determine the time required to cool the sphere from 900°C to 300°C if the velocity and temperature of the nitrogen are V = 5 m/s and T∞ = 25°C.

(b) Accounting for the effects of both convection and radiation, with ϵ = 0.6 and Tsur = 25°C, determine the time required to cool the sphere. Explore the effects of the flow velocity on your result.